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INTER-NOISE 200728-31 AUGUST 2007ISTANBUL, TURKEY

Numerical noise prediction: application to radial fans

Yilmaz Dogana, Esra Sorguvenb, Faruk Bayraktarc, Kenan Y.Sanliturkd

Arçelik A..R & D DepartmentVibration & Acoustic TechnologiesTuzla, 34950 IstanbulTURKEYABSTRACTIn this study, aerodynamics and aeroacoustics of two radial fans are investigated by using ahybrid computational aeroacoustics method. Unsteady turbulent flow field of both fans issimulated with large eddy simulation (LES). Acoustic sources are computed based on thepressure fluctuations. Inhomogeneous wave equation, which accounts for the propagation,diffraction and scattering of the acoustic sources inside the volute, is solved to determinethe far field sound pressure level with the boundary element method. Numerically obtainedsound pressure level distributions are in a good agreement with experimental data. Soundpressure level distribution in narrow band frequency spectrum, directivity of the acousticwaves and the overall sound power level are predicted numerically with a high accuracy.Furthermore, results of the LES provide an insight to the turbulent flow and noisegeneration mechanisms.1 INTRODUCTIONFlow induced noise prediction in industrial applications is essential in order to control thenoise emission and to comply with the noise regulations and consumer demands.Experimental methods involve drawbacks like time and investment expenses andmeasurement errors like reflection problems. With the improvement in computationaltechnology, aomputational aeroacoustics (CAA) provides a proper model for noise predictionand reduction. Especially hybrid CAA methods are efficient and inexpensive, since theysolve for the different scales of aerodynamics and aeroacoustics separately.Studies on aeroacoustics began after the 2ndWorld War, as the civil aircraft technologyhas evolved. In his acoustic analogy, Lighthill [1, 2] derived an inhomogeneous waveequation to describe the jet noise, which arises due to turbulent pressure fluctuations, fordescribing the radiation of the sound field generated by turbulent flow. Curle [3] contributedthe effect of solid surfaces on sound generation and by Ffowcs Williams and Hawkings [4]the effect of moving solid surfaces on sound generation is contributed to the acousticanalogy. Numerical methods for the prediction of fan noise usually account for tonal andbroadband noise separately. Gutin[5], Carolus [6] and Bommes et. al. [7] have made notablecontributions to the aerodynamics and the acoustics of the fans. A recent review oncomputational aeroacoustics has been provided by Colonius and Lele [8].

C Email address: faruk.bayraktar@arcelik.comC Email address: sanliturk@itu.edu.trStudies involving analysis, prediction and reduction of fan noise are active research areasbecause of the widespread use of axial and centrifugal fans in industry. Lin et. al. [9]designed a small Forward–Curved (FC) centrifugal fan under the space limitations ofnotebook computers with the emphasis on the blade shape, blade inlet angle and the outletgeometry of the housing and the flow patterns throughout the fan are visualized usingnumerical techniques. Jeon et. al. [10] developed a method to calculate the unsteady flowfields and Aeroacoustic sound pressure in the centrifugal fan of a vacuum cleaner: Unsteadyflow-field data are calculated by the vortex method. The sound pressure is then calculated byan acoustic analogy. Nallasamy et. al. [11] studied the rotor wake turbulence statorinteraction broadband noise. The computations employ the wake flow turbulence informationfrom computational fluid dynamic solutions. Gérard et. al. [12] developed an inverseAeroacoustic model aiming at reconstructing the aerodynamic forces (dipole strengthdistribution) acting by the fan blades at multiples of the Blade Passing Frequency (BPF) onthe fluid that relates the unsteady forces to the radiated sound field. Velarde et. al. [13]studied the experimental determination of the tonal noise sources in a centrifugal fan.Özyörük et. al. [14] developed a frequency-domain method for predicting sound fields ofducted fans based on the solution of the frequency-domain form of the Euler equationslinearized about an axisymmetric non-uniform background flow. Wu et. al. [15] developed asemi-empirical formula capable of simulating both narrow and broad band sounds of thespectra for the tested axial flow fans in a free-field. Wu et. al. [16] also developed a computermodel for estimating the noise performance of an engine cooling fan assembly. The computermodel thus obtained is validated experimentally on five sets of completely different enginecooling fan assemblies. Velarde et. al. [17] studied a three-dimensional numerical simulationof the complete unsteady flow on the whole impeller-volute configuration of a centrifugalfan. It is claimed that, numerical results have been confirmed using experimentalinvestigations, showing a good agreement.In this paper, aerodynamics and aeroacoustics of two radial fans are investigated viaCAA. For this purpose a hybrid method is employed. Aeroacoustic computations of both fansare performed in two steps: i) computing the unsteady flow field and ii) computing theacoustic pressure fluctuations in the far field in the frequency domain. Flow field is solvedwith Large Eddy Simulation (LES) where the large and energetic scales of turbulence areresolved and the small and dissipative scales are modeled. Acoustic sources are computedbased on the turbulent unsteady flow field. Finally, the wave equation is solved to determinethe far field sound pressure level. It is shown that the numerical results of the turbulentunsteady flow and noise emission are in good agreement with the experimental results.Computing the aerodynamics and aeroacoustics data of both fans also shows how the CAAmethods provide an insight to the turbulent flow and the noise generation mechanisms andhow these can be utilized to decrease the overall sound pressure level of a fan.2 COMPUTATIONAL METHODS2.1 Computational Fluid DynamicsAn overview of the modern CAA methods is given in Fig.1. As can be seen in this figure,modern CAA techniques can be separated into two steps; the first step being thedetermination of the unsteady flow data (flow calculation) and the second step being thecomputation of the acoustic data (acoustic calculation). Flow calculation can be performedwith unsteady Reynolds Averaged Navier-Stokes equations (uRANS), Large EddySimulation (LES) or Direct Numerical Simulation (DNS). Flow parameters can be divided asfollows:φis the mean value,.turbφ. is the turbulent part and.acφ. is the acoustic part of theflow parameters. Although uRANS requires relatively low computational time and power, itcannot handle the unsteady flow accurately. However DNS aims to solve the Navier-Stokesequation without any modeling approximations and aims to resolve the whole range of timeand length scales; from integral scales to Kolmogorov scales. With DNS, one can solve allthe scales and obtain the mean, turbulent and acoustic parts of the flow parameters. The maindisadvantage of such methods is the enormous computational cost of such direct calculations,this being the main reason for which only relatively simple flow configurations at modestReynolds numbers were studied.

Figure1: Overview of the modern CAA methods

In this paper LES method, which resolves the large and energetic scales of turbulence andmodels the small and dissipative scales, is used to calculate the unsteady flow field.2.2 Investigated fansTwo radial fan systems with their volute and inlet and outlet pipes are investigated. Thefirst radial fan system- called”Fan I” has a higher sound pressure levels than the radial fansystem called “Fan II”.Both of the investigated radial fan systems are nearly 50 cm long and have a rotationalspeed of 2800 rpm (Fig. 2). The impeller of Fan I with 37 forward curved blades has an outerdiameter of 130 mm and a depth of 55 mm. Accordingly, Reynolds number based on theblade tip diameter and speed istipRe=136,000 and Mach number at the tip istipM=0.05.The impeller of Fan II with 25 forward curved blades, has an outer diameter of 120 mm and adepth of 85 mm. Accordingly, Reynolds number based on the blade tip diameter and speed istipRe=110,000 and Mach number at the tip istipM=0.05.

Computational mesh for individual fans comprises approximately 2.5x106controlvolumes (Fig. 2). Although the total number of control volumes seems to be insufficient foran LES, the density of the control volumes is increased in the vicinity of the fan blades,where most of the sound emission occurs. Cell distribution is forced to be finer on the wallsto resolve the boundary layer and in the neighborhood of the blade. The dimensionless walldistance y+ is kept about 1 over the whole propeller surface and the use of a wall model isomitted. Mesh elements surrounding the impeller are structured and hexahedral, whereastetrahedral elements are used in the volute.The computational domain is divided into two zones, one surrounding the rotatingimpeller and other surrounding the stationary volute. Zones are coupled via a sliding interfaceand mass balance is forced across the sling interface. In order to minimize the interpolationerrors, the ratio of the control volumes across the sliding interface is kept below 4:1. Theemployed boundary conditions are no-slip at the walls, constant total pressure at the inlet andconstant static pressure at the outlet. The computational domain is initialized with the flowdata obtained from a steady RANS simulation, in order to accelerate convergence. Spatialdiscretization is performed with the 2nd order central differencing scheme and temporaldiscretization with the 2nd order implicit dual time stepping scheme. The aerodynamical andacoustic time steps are set equal as 1x10-4s, i.e. about 1° of rotation of fan is simulated ateach time step.Pressure fluctuations on the surfaces are recorded after nearly five rotations of the fans, sothat only statistically steady data are evaluated in the acoustic computation. After thestatistically steady state is achieved, flow simulations are continued further for about 5revolutions of the Fan I, i.e. for 0.107 seconds and about 3 revolutions of the Fan II, i.e. for0.064 seconds. The dipoles are computed depending on the flow data of these lastrevolutions. Among the three types of sound sources (i.e. monopoles, dipoles andquadrupoles) the dipole terms dominate the sound emission in a turbomachinery [18].2.3 Acoustic ComputationThe aeroacoustic modeling is performed with the aeroacoustic module of thevibroacoustic solver LMS Sysnoise. Sysnoise is capable of solving wave equation in interiorand exterior domains with different discretization techniques like Boundary Element Method(BEM) and Finite Element Method (FEM) [19].The input for aeroacoustic module is time-dependent pressure and velocity data which areobtained from the CFD solution. The flow data are used to calculate the acoustic source termson the right hand side of the wave equation.In order to model the interior and the exterior domains simultaneously, the Multi-DomainBEM analysis is performed. The analysis consists of two models which are the Direct BEMInterior and the Direct BEM Exterior models. Both models are linked at the openings of theduct, through a fluid-fluid coupling. The coupling satisfies the boundary condition at theopenings, equivalent to ambient pressure boundary condition. The boundary conditionapplied on the duct surface is the rigid wall boundary condition. The stationary dipole sourceson the duct surface are defined as discrete sound sources on the nodes of the acoustic mesh.3 RESULTS3.1 Computational Fluid DynamicThe following figures aim to give an overview of the flow around the fan and inside thevolute.

Figure 3 shows the instantaneous magnitude of the vorticity at a cross-section along theflow domain. The vorticity is produced mainly on the blades; especially at the blade tip andon the trailing edge. It is then transported further with the flow through the pipe. From figuresit can be seen that although the vorticity produced is similar in both fan impellers, in Fan I thevorticity is transported further into the outlet pipe.3.2 Computational Aero Acoustics

Computational grid for Aeroacoustic calculations is created using the 3D drawing/FEMsolver in I-DEAS. Aeroacoustic computational grid is coarse; hence, an external MATLABinterface code is used for interpolation between fine CFD mesh and coarse Aeroacousticmesh.Aeroacoustic computation involves two steps:i) Assigning the dipole sources over the Aeroacoustic meshii) Coupling between the Multi Domain Boundary Element Method (MDBEM) – Interiorand MDBEM – exterior to model the acoustic modes of the cavity.

Figure 5: Coupling procedure for fans

In Fig. 5, MDBEM Exterior and MDBEM Interior models are shown for Fan I. Withassigned dipoles on Interior model, both models are coupled via openings to calculate thecavity modes of the volute and also scattering phenomenon.ω(1/s)

Figure 6: I-BEM model and sound radiation model for current designIn Fig. 6, a fictitious surface used in both experiments and numerical calculations isshown. The physical and numerical systems have a reflective surface and field points tomeasure sound intensity.Numerical results of the two radial fans are summarized in Fig. 8. The acoustical resultsare obtained according to sound intensity mapping. A field point mesh is created for bothfans, which corresponds the microphone positions of the experiments.

Fan II has a lower sound power level with respect to that of Fan I (Fig. 8). With the samecolor scale range, the directivity shows different characteristics from one cavity frequency toanother. However, the magnitude of the sound pressure levels is different, but directivitypatterns are very similar for the two different fans.4 MEASUREMENTS AND COMPARISION WITH NUMERICAL RESULTSSound intensity measurements are performed for the two fans over a rectangular box inwhich fans are located. Sound intensity is the time-averaged product of the pressure andparticle velocity. Therefore, it is possible to measure pressure gradient with two closelyspaced microphones and relate it to particle velocity.The use of sound intensity rather than sound pressure to determine the sound powerallows to perform the measurement in situ. The sound power is the average normal intensityover a surface enclosing the source, in this case fan-volute system, multipled by the surfacearea. The fictitious surface and the reflective floor are the same as in the numericalcomputation (Fig. 6).Fan

The experimental Sound Pressure Level (SPL) curve is smoother than the numericalcurve. The reason for this is related to the amount of data used to obtain these results: In theexperiments, the acoustic signal is measured for about 10 s. However, in the simulation thetotal time for the acoustic evaluation is about 0.107 s for Fan I and 0.064 s for Fan II whichcorresponds to about 5 and 3 rotations of the propeller. In the experiments the acoustic signalof about 500 rotations is evaluated. Since the frequency analysis is performed with far lessdata in the simulation than what is available in the experiment. Therefore, the numerical SPLcurve has more fluctuations than the experimental curve. If the acoustic computation iscarried out for longer time, these fluctuations will disappear, but the general shape of thecurve will remain the same.

Figure 10: Sound pressure level spectrum from computations and experiments of Fan I

As can be seen in Fig.10, the numerical prediction of the acoustic signal in the far fieldmatched the experimental measurements satisfactorily for Fan I.

As seen in Fig.11 that the acoustic prediction agrees well with the experimentalmeasurements in the case of Fan II.From Figures 12-13, one can see that for both fans, the CAA-tool is tested with highaccuracy. The first test case is the prediction of the flow noise of a radial fan currently used inlaundry dryers with high SPL. Simulations of the flow in the flow domain of fan-volutesystem show that LES is a reliable flow simulation method. The aerodynamicalcharacteristics of the flow are predicted with high accuracy. Consequently, the acousticprediction and directivity of the sound agrees well with the experimental measurements.

Figure 12: Numerical and experimental sound intensity mapping over the field point for Fan I (270Hz and 520Hz respectively (1/12 octave band))